Как это подробно) cos(0.5arctg(8/15)-0.5pi)=?

cos(0.5arctg(8/15)-0.5pi) - ?
arctg(8/15) = x  угол
tg(arctg(8/15)) = 8/15
значит:
a = 8  катет
b = 15 катет
c = √(8²+15²) = √(64+225) = √289 = 17 гипотенуза
х = arctg(8/15)  угол между b и c
cos(0.5x-pi/2) = sin(0.5x) =>
=> cos(0.5arctg(8/15)-0.5pi) = sin(0.5arctg(8/15))
sin(x) = sin(arctg(8/15)) = 8/17
cos(x) = cos(arctg(8/15)) = 15/17
Формулa половинного аргумента:
sin²(x/2) = (1 - cosx)/2
sin²(x/2) = (1 - 15/17)/2
sin²(x/2) = 1/17
sin(x/2) =  ±1/√17 = ±√17/17
sin(x/2) = sin(0.5arctg(8/15)) = cos(0.5arctg(8/15)-0.5pi) =1/√17 = √17/17
cos(0.5arctg(8/15)-0.5pi) = 1/√17 = √17/17
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